Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2605.08607 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910203564261376 |
|---|---|
| author | Khukhro, Evgeny Shumyatsky, Pavel |
| author_facet | Khukhro, Evgeny Shumyatsky, Pavel |
| contents | For an element $g$ of a group $G$, a right Engel sink of $g$ is a subset of $G$ containing all sufficiently long commutators $[...[[g ,x],x],\dots ,x]$ for all $x\in G$. A left Engel sink of $g$ is a subset of $G$ containing all sufficiently long commutators $[...[[x ,g ],g ],\dots ,g]$ for all $x\in G$. Using the classification of finite simple groups we prove that if a finite group $G$ has an element $g$ such that $G=[G,g]$, then the order of $G$ is bounded in terms of a right Engel sink of $g$, as well as in terms of a left Engel sink of $g$. Earlier Guralnick and Tracey proved this in the case where $g$ is an involution without using the classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08607 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On finite groups containing an element whose Engel sink is small Khukhro, Evgeny Shumyatsky, Pavel Group Theory For an element $g$ of a group $G$, a right Engel sink of $g$ is a subset of $G$ containing all sufficiently long commutators $[...[[g ,x],x],\dots ,x]$ for all $x\in G$. A left Engel sink of $g$ is a subset of $G$ containing all sufficiently long commutators $[...[[x ,g ],g ],\dots ,g]$ for all $x\in G$. Using the classification of finite simple groups we prove that if a finite group $G$ has an element $g$ such that $G=[G,g]$, then the order of $G$ is bounded in terms of a right Engel sink of $g$, as well as in terms of a left Engel sink of $g$. Earlier Guralnick and Tracey proved this in the case where $g$ is an involution without using the classification. |
| title | On finite groups containing an element whose Engel sink is small |
| topic | Group Theory |
| url | https://arxiv.org/abs/2605.08607 |